An implementation of hypothesis testing in an extended Rasch modeling framework,
including sample size planning procedures and power computations. Provides 4 statistical tests,
i.e., gradient test (GR), likelihood ratio test (LR), Rao score or Lagrange multiplier test (RS),
and Wald test, for testing a number of hypotheses referring to the Rasch model (RM), linear
logistic test model (LLTM), rating scale model (RSM), and partial credit model (PCM). Three
types of functions for power and sample size computations are provided. Firstly, functions to
compute the sample size given a user-specified (predetermined) deviation from the hypothesis
to be tested, the level alpha, and the power of the test. Secondly, functions to evaluate the
power of the tests given a user-specified (predetermined) deviation from the hypothesis to be
tested, the level alpha of the test, and the sample size. Thirdly, functions to evaluate the
so-called post hoc power of the tests. This is the power of the tests given the observed
deviation of the data from the hypothesis to be tested and a user-specified level alpha of the
test. Power and sample size computations are based on a Monte Carlo simulation approach. It is
computationally very efficient. The variance of the random error in computing power and sample
size arising from the simulation approach is analytically derived by using the delta method.
Additionally, functions to compute the power of the tests as a function of an effect measure
interpreted as explained variance are provided.
Draxler, C., & Alexandrowicz, R. W. (2015),
An implementation of hypothesis testing in an extended Rasch modelling framework including sample size planning procedures and power computations. Provides 4 statistical tests, i.e. gradient test (GR),likelihood ratio test (LR), Rao score or Lagrange multiplier test (RS), and Wald test, for testing a number of hypotheses referring to the Rasch model (RM), linear logistic test model (LLTM), rating scale model (RSM), and partial credit model (PCM).Three types of functions for power and sample size computations are provided. Firstly, functions to compute the sample size given a user-specified (predetermined) deviation from the hypothesis to be tested, the level alpha, and the power of the test. Secondly, functions to evaluate the power of the tests given a user-specified (predetermined) deviation from the hypothesis to be tested and the level alpha of the test. Thirdly, functions to evaluate the so-called post hoc power of the tests. This is the power of the tests given observed deviation of the data from the hypothesis to be tested and a user-specified level alpha of the test. Power and sample size computations are based on a Monte Carlo simulation approach. It is computationally very efficient. The variance of the random error in computing power and sample size arising from the simulation approach is analytically derived by the delta method.